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Forward-Chaining Partial-Order Planning Amanda Coles, Andrew Coles, Maria Fox and Derek Long (to appear, ICAPS 2010)

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Summary Forward-chaining planning eliminates the threat resolution of POP, at the price of over- commitment. Issues arise in temporal planning, due to needless ordering constraints leading to backtracking. Can modify a forward-chaining approach to construct a partial-order, avoiding this. Further, can modify a TRPG heuristic to encourage search to find lower makespan plans. Implemented and evaluated in the planner POPF

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Overview (Temporal) Forward-Chaining Planning Issues with using a Total Order Reducing Commitment Heuristic Guidance for Lower Makespan Plans EvaluationConclusions

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Forward Chaining Temporal Planning A state S is a tuple of: Propositional Facts Propositional Facts Values of task variables Values of task variables A Queue of actions that have not yet finished A Queue of actions that have not yet finished The Plan to reach S The Plan to reach S The Constraints on the steps in P The Constraints on the steps in P The plan consists of the starts and ends of actions: A and A denote the start/end of A, resp. A and A denote the start/end of A, resp.

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light_match match1 light m1 ¬light m1 mend_fuse fuse1 match1 0: light_match_start match1 1: mend_fuse_start fuse1 match1 2: mend_fuse_end fuse1 match1 3: light_match_end match1 lms mfs1mfe1 lme 8.0 -8.0 -0.01 - 5.0 5.0 -0.01 Epsilon separation (0.01) Simple Example

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Overview (Temporal) Forward-Chaining Planning Issues with using a Total Order Reducing Commitment Heuristic Guidance for Lower Makespan Plans EvaluationConclusions

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Issues with Using a Total Order To resolve threats, F.C. planning uses a total order. When applying an action A: A cannot violate preconditions of earlier actions, as it comes after them (demotion); A cannot violate preconditions of earlier actions, as it comes after them (demotion); Subsequent actions cannot delete its preconditions, as A comes sooner (promotion) Subsequent actions cannot delete its preconditions, as A comes sooner (promotion) The drawback is that needless ordering constraints are added: If A does not interfere with the preceding step, it still must come after it. If A does not interfere with the preceding step, it still must come after it. Motivates partial-order lifting, but this first needs a solution to be found.

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Total Orders of Start/End Actions Two actions, A and B: B is longer than A; B is longer than A; No interaction between A and B ; No interaction between A and B ; But, B must precede A But, B must precede A The planner chooses a (partial) plan: A B B

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A B B A A -0.01 2 -2 5 -5 -0.01 A was added to the plan before B, theyBecause A was added to the plan before B, they are ordered as shown (in a total-order). are ordered as shown (in a total-order). But, Awill not be applicable until after BBut, Awill not be applicable until after B The planner will have to backtrack, over all the intermediateThe planner will have to backtrack, over all the intermediate decisions, and add B to the plan earlier than A decisions, and add B to the plan earlier than A.

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Overview (Temporal) Forward-Chaining Planning Issues with using a Total Order Reducing Commitment Heuristic Guidance for Lower Makespan Plans EvaluationConclusions

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Reducing Commitment Record additional information at each state concerning which steps achieve / delete / depend on each fact. Use this information to commit to fewer ordering constraints Still resolve threats based on the intuition of forward-chaining expansion: new actions cannot threaten the preconditions of earlier actions.

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Extending the State: Propositional To capture ordering information we add: F +, F -, where F + (p) (F - (p)) is the index of the of the step that most recently added (deleted) p FP, where FP(p) is a set of pairs : denotes that step i has an instantaneous condition on p ( at start or at end ) denotes that step i has an instantaneous condition on p ( at start or at end ) denotes that step i marks the end of an action with an over all condition on p denotes that step i marks the end of an action with an over all condition on p

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Starting an Action A at Step i For each at start condition p: t(F + (p)) + ε t(i) For each at start del. effect p, assign F - (p) = i, t(F + (p)) + ε t(i), and in FP(P), t(j) + d t(i) For each at start add effect p, assign F + (p) = i, and if F - (p) i, t(F - (p)) + ε t(i) For each over all condition p: If F + (p) i, t(F + (p)) t(i) (To apply the end of an action: similar process, but without over all conditions) A

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A B B A A -0.01 2 -2 5 -5 -0.01 0.00: (action B) [5.00] 3.01: (action A) [2.00]

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Extending the State: Numeric For numbers we are a little more strict: V eff, where V eff (v) is the step of the action to most recently have an effect on v VP, where VP(v) contains steps that depend on the value of v, each step i such that: i has a precondition on v, or is the start of an action whose duration constraint contains v; or, i has a precondition on v, or is the start of an action whose duration constraint contains v; or, i has an effect that depends on v i has an effect that depends on v VI, where VI(v) is a set of pairs (s,e), marking the start/end indices of actions in the event queue (Q) with an over all condition depending on v (Also, V cts to handle linear continuous numeric change – see paper for details.)

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Starting an Action A at Step i: For each variable v relevant to at start conditions, effects, or the actions duration: t(V eff (v)) + ε t(i) For each v on which A has an at start eff, apply the effect to V, and: (s,e) in VI(v), t(s) + ε t(i) and t(i) + ε t(e) For each variable v relevant to an over all, add (i,j) to VI(v), and if was not relevant to the start of A: t(V eff (v)) + ε t(i) A

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Overview (Temporal) Forward-Chaining Planning Issues with using a Total Order Reducing Commitment Heuristic Guidance for Lower Makespan Plans EvaluationConclusions

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Heuristic Guidance Have seen how the search space can be modified to reduce excessive ordering constraints; There is still no pressure to prefer choices that lead to a partial-order with a lower makespan Could use partial-order lifting a posteriori for similar quality results? Could use partial-order lifting a posteriori for similar quality results? Given we know the makespan implications of action choices, how can we factor this into the decision making during search?

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Revisiting the Temporal RPG The Temporal RPG consists of time-stamped fact and action layers. To evaluate a state S: Fact layer f=0.0 contains the facts in S; Fact layer f=0.0 contains the facts in S; Action layer a=0.00 contains actions whose preconditions are satisfied in f=0.0; Action layer a=0.00 contains actions whose preconditions are satisfied in f=0.0; Effects of actions appear in the next layer; the end of an action A is delayed until dur(A) after A start first appears. Effects of actions appear in the next layer; the end of an action A is delayed until dur(A) after A start first appears. What about the extra information we now have in S?

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Bounding Preconditions and Effects on Facts When adding actions to the partial order, for a proposition p: Any action requiring p to satisfy a precondition will need to come after t(F + (p)) and t(F - (p)) Any action requiring p to satisfy a precondition will need to come after t(F + (p)) and t(F - (p)) Any action with an add (delete) effect on p will need to come after t(F - (p)) ( t(F + (p)) resp.) Any action with an add (delete) effect on p will need to come after t(F - (p)) ( t(F + (p)) resp.) From checking temporal constraints, we have a lower-bound on each step, t min (i) Thus, the earliest point we can use p is: l(p) = max { t min (F + (p)), t min (F - (p)) + ε }

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Bounding (continued) Similarly, for each numeric precondition/effect referring to a variable set vars, it cannot be used until: L(vars) = max v in vars t min (v eff (v)) With these bounds, for any state S, we can build a TRPG starting at time zero: Delay fact p until layer L(p) Delay fact p until layer L(p) Delay numeric preconditions/effects until L(vars) for their respective variable sets Delay numeric preconditions/effects until L(vars) for their respective variable sets Then, actions which do not interfere with existing choices will appear sooner in the TRPG.

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Overview (Temporal) Forward-Chaining Planning Issues with using a Total Order Reducing Commitment Heuristic Guidance for Lower Makespan Plans EvaluationConclusions

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Evaluation Planner POPF, based on the code for COLIN (IJCAI09) First test: Control: run COLIN, then apply partial-order lifting to the solution Control: run COLIN, then apply partial-order lifting to the solution POPF, but using the original heuristic from COLIN. POPF, but using the original heuristic from COLIN. Second test, also considering domains with deadlines: COLIN then partial-order lifter COLIN then partial-order lifter POPF, new heuristic. POPF, new heuristic.

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Test 1: Time Taken

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Test 1: Makespan

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Test 2: Time Taken

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Test 2: Makespan

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Test 2: Time Taken (Deadlines)

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Conclusions Have shown how a partial-order can be expanded in a forwards direction; Adapting the heuristic allows one to trade time performance for a reduction in makespan; In domains with deadlines, performance is: substantially improved (fivefold improvement in coverage in the Satellite variants). In domains with deadlines, performance is: substantially improved (fivefold improvement in coverage in the Satellite variants). In the paper: approach also works with domains containing linear-continuous change

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